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Physics problems: dynamics

Newton's laws

 

Problem 3.

You are driving along an empty straight road at a constant speed u. At some point you notice a tall wall at a distance D in front of you. Would it require a larger force to (a) continue moving straight and decelerate to a full stop before the wall, or (b) turn left or right to avoid the wall? (to make the calculation easier assume that the turn is done at a constant speed along a circular path).

Solution

 

Problem 8.

As part a of the drawing shows, two blocks are connected by a rope that passes over a set of pulleys. The block 1 has a weight of 400 N, and the block 2 has a weight of 600 N. The rope and the pulleys are massless and there is no friction.

(a) What is the acceleration of the lighter block?

(b) Suppose that the heavier block is removed, and a downward force of 600 N is provided by someone pulling on the rope, as part b of the drawing shows. Find the acceleration of the remaining block.

Solution

 

Problem 9.

Part a of the drawing shows a block suspended from the pulley; the tension in the rope is 80 N. Part b shows the same block being pulled up at a constant velocity. What is the tension in the rope in part b ?

 

 

Solution

 

Problem 11.

A box is sliding up an incline that makes an angle of 20 degrees with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.2. The initial speed of the box at the bottom of the incline is 2 m/s. How far does the box travel along the incline before coming to rest?

Solution

 

Problem 12.

A block weighing 80 N rests on a plane inclined at 30 degrees to the horizontal. The coefficients of static and kinetic friction are 0.2 and 0.1 respectively. What is the minimum magnitude of the force F, parallel to the plane, that will prevent the block from slipping?

Solution

 

Problem 16.

A rocket of mass kg is in flight. Its thrust is directed at an angle of 60 degrees above the horizontal and has a magnitude of . Find the magnitude and direction of the rockets acceleration. Give the direction as an angle above the horizontal.

Solution

 

 

 

 

 

Problem 17.

The speed of a bobsled is increasing because it has an acceleration of . At a given instant in time, the forces resisting the motion, including kinetic friction and air resistance, total 500 N. The mass of the bobsled and its riders is 300 kg.

(a) What is the magnitude of the force propelling the bobsled forward?

(b) What is the magnitude of the net force that acts on the bobsled?

Solution

 

Problem 18.

A person in a kayak starts paddling, and it accelerates from 0 to 0.8 miles/hour in a distance of 0.8 km. If the combined mass of the person and the kayak is 80 kg, what is the magnitude of the net force acting on the kayak?

Solution

 

Problem 25.

A tension of 6000 Newtons is experienced by the elevator cable of an elevator moving upwards with an acceleration of . What is the mass of the elevator?

Solution

 

Problem 26.

What conditions are necessary for an object to move with constant velocity?

What conditions are necessary for an object to move with constant acceleration?

Solution

 

Problem 28.

Is it easier to move a heavy box that is sitting on the ground by (a) pulling the box from a rope that makes an angle with the surface or (b) by pushing the box with a force that makes the same angle (but pointing downwards) with the surface?

Solution

 

Problem 30.

A spaceship is on a straight-line path between Earth and moon. At what distance from the Earth is net gravitational force on the spaceship zero?

Solution

 

 

 

 

 

Problem 32.

The athlete, who has a mass of 100 kg, can throw a 500 g ball with a speed of 10 m/s. The distance through which his hand moves as he accelerates the ball forward from the rest until he releases it is 1.0 m. What constant force must the athlete exert on the ball to throw it with this speed?

Solution

 

Problem 34.

A 10.0 kg block is towed up an inclined at with respect to the horizontal. The rope is parallel to the incline and has a tension of 100 N. Assume that the block starts from rest at the bottom of the hill, and neglect friction. How fast is the block going after moving 40 m up the hill?

Solution

 

Problem 35.

A 0.01 kg object is moving in a plane. The x and y coordinates of the object are given by and y . Find the net force acting on the object at t=2 s.

Solution

 

Problem 36.

An automobile weighing 3200 lbs. is on a road which rises 10 ft. for each 100 feet of road. What force tends to move the car down the hill?

Solution

 

Problem 37.

At 20 meters long rope attached at the top and the bottom of a flag pole is pulled 2 meters away from the pole by a 100 newton force acting at right angles to the pole at its mid point. What is the tension on the segments of the rope on each side of the 100 newton force?

Solution

 

Problem 38.

A crane cable that is capable of withstanding 22,000 N is attached by a hook to  a 2,000 kg block that is resting on the ground. The cable initially starts lifting the block at the maximum acceleration that the cable can withstand for 4 sec.  It then continues to raise the block at constant velocity for further 2 sec. At this time the block slips off the hook at the end of the cable.
Calculate:

(1) the tension in the cable when the block is moving at constant velocity;

(2) the maximum acceleration that the cable can withstand;

(3) the maximum height that the block reaches above ground.

Solution

 

 

 

 

 

Problem 46.

A hotel guests starts to pull an armchair across a horizontal floor by exerting a force of 91 N 15 degrees above the horizontal.  The normal force exerted by the floor on the chair is 221 N up.  The acceleration of the chair is 0.076 .  Determine the mass of the chair.

Solution

 

Problem 47.

A man who has a mass of 100 kg, is skateboarding at 8.0 m/s when he smacks into a brick wall and comes to a dead stop in 0.4 seconds. What is his deceleration? What is force on the man due to his deceleration?

Solution

 

Problem 50.

An object with mass of 630 g is hung on a spring. What is the force of the object acting on the spring?

Solution

 

Problem 52.

A 35 kg crate undergoes a horizontal acceleration of acceleration on a level surface when pulled by a 65.0 N force. What is the coefficient of kinetic friction between the crate and the surface?

Solution

 

Problem 53.

A block of mass 13.6 kg is sliding at an initial velocity of 4.65 m/s along horizontal surface to the right. The surface has a coefficient of kinetic friction of 0.254. How far will it slide before coming to rest?

Solution

 

Problem 55.

What is the magnitude of the force needed to maintain the circular motion of a 45-kg cyclist riding a 40-kg bicycle at 12.5 m/s around a 35.0-m radius circular track.

Solution

 

Problem 56.

Two force force and resultant force of magnitude 5N each, inclined to each other at 60 degrees, act on a body. Find the resultant force acting on the body.

Solution

 

Problem 57.

A passenger of mass m=72.2 kg stands on a platform  scale in an elevator cab.

(a)what does the scale read if the cab is stationary or moving upward with a constant speed of 0.50 m/s?

(b)what does the scale read if the cab accelerates downward at acceleration?

Solution

 

 

 

 

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