Particle Newtonian Mechanics - Review Problems

RP5-1) What is equilibrium? Check all that apply.

RP5-2) What are Newton’s first, second and third laws? Below are statements of Newton's laws. For each, choose which law.

A body acted on by an imbalance of forces will accelerate. The amount of acceleration is inversely proportional to its mass.
       

An object at rest tends to stay at rest and an object in motion tends to stay in motion at constant speed in a straight line.
       

For every force of action, there is an equal and opposite reaction.
       

RP5-3) What is a body's equation of motion?  

RP5-4) The velocity of a particle is given by the v-t (velocity-time) graph shown. Which of the given F-t (force-time) graphs best represent the corresponding net resultant force experienced by the particle as a function of time?

RP5-5) Is the normal force on a body always equal to its weight?    

RP5-6) The normal force is always perpendicular or normal to what? Click all that apply.

RP5-7) A boy swings on a rope, as shown in the figure. Which of the following forces are acting on the boy? Check all that apply.

RP5-8) A constant force pushes a block that slides on a frictionless surface. The block is initially at rest and the force (F) acts on the block for t_f seconds. The block reaches a final speed of v_f. To reach the same final speed with a constant force that is only half as big (F/2), the force would have to act on the block for _________ seconds.

Suppose that this time the block, instead of starting from rest, starts from an initial constant velocity of v_o before the force (F) is applied. After the force is applied for t_f seconds, the increase in the block's speed is...

Consider two blocks, initially at rest, similar to the block above. The first block is pushed by a constant force (F) and has a mass of m. It reaches a speed of v_f in t_f seconds. The second block is pushed by a constant force (F) and has a mass of 2m. The speed of the second block is ___________ if it is pushed for t_f seconds.

RP5-9) What is the difference between the static friction force and the limiting static friction force?

RP5-10) What is the equation that we use to calculate the kinetic friction force?

RP5-11) You are riding a bike along a flat horizontal road. Draw the friction force acting on the front and rear tires for the following situations. Indicate the relative magnitudes of the friction forces by varying the length of the vectors.

1. You are accelerating forward.  

 

 

 

2. You are traveling at a constant speed.  

 

 

 

3. You stop pedaling and apply the front brakes.  

 

 

 

RP5-12) Imagine that you are swinging a bucket full of water in large circle within the vertical plane. What keeps the water from falling out?  

RP5-13) A car pulls a boat on a trailer. The mass of the boat and the final velocity reached are given in the figure. In each situation, the car increases its speed at a constant rate and takes the same amount of time to reach its final velocity. Each case starts from the same initial. Input the case letters from largest to smallest hitch force. Do not separate the letters with comma's or other punctuation mark.

RP5-14) The 35-kg block shown is subjected to forces F₁ = 100 N and F₂ = 75 N. If the block is originally at rest, determine the distance it slides in 10 seconds. The coefficient of kinetic friction between the crate and the surface is μ_k = 0.4 and the forces are applied at angles of θ = 20^o and φ = 35^o.

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

RP5-15) The figure shows a conveyer belt system used to transport boxes. Determine the expression for the maximum speed the box may have in order to traverse the curve without slipping relative to the belt. The design parameters are the radius of the curve and the static coefficient of friction between the box and the belt.

The solution will be simplest if the following coordinate system is used.

RP5-16) Arm OA rotates counterclockwise with a constant angular velocity of 5 rad/s. As the arm passes the horizontal position, a 5-kg ball is placed at the end of the arm. As the arm moves upward, the ball begins to roll, with negligible rolling resistance, towards the pivot O. It is noted that at θ = 30^o the ball is 0.8 meters from the pivot and moving towards O along the length of the arm. The ball moves with a speed of 0.5 m/s along the bar. What is the normal force that the arm applies to the ball at this instant?

The solution will be simplest if the following coordinate system is used.

RP5-17) A truck is forced to stop unexpectedly. If the truck is initially traveling at 40 mph and is able to stop in 180 ft with a constant deceleration. Determine if the 500-lb crate reaches the end of the flat bed if it is located d = 6 ft behind the front of the bed. The coefficient of kinetic and static friction between the crate and the bed are 0.9 and 0.6 respectively.