Question

On the left are listed various physics problems. On the right are listed various approaches to solving physics problems. For each item on the left, choose the best approach on the right and write its letter on the blank line on the left.

__ A large crane lifts a grand piano in a crate from the ground to the top of a tall building. You desire to find how much work the crane did. __ A bird hits and sticks in a slowly spinning wheel. You desire to find how this affects the motion of the wheel. __ A flywheel is spinning and has nothing acting on it but friction. You know the numerical value for the effect of friction. You desire to find how long it will take for the flywheel to come to a stop. __ A truck hits a stationary car head on, and you are able to estimate their velocities right after they hit. You desire to calculate if the truck was initially going over the speed limit. __ A small block sits motionless on a tilted ramp and remains motionless because of friction. You desire to find the coefficient of friction. __ A spring-loaded dart gun has a known spring constant and compressions distance. You desire to calculate the highest that a dart can be shot from this gun. __ A rocket has a known mass and upward thrust. You desire to find the rocket’s acceleration. __ A spaceship collides with a small asteroid and you desire to find how this affects the speed of the spaceship. No spinning motion occurs. __ A figure skater is spinning and brings her arms in. You desire to find how fast she is spinning at the end. __ One end of a diagonal ladder sits on the ground and the other end of the ladder hangs from a vertical rope attached to a crane. Everything remains motionless. You desire to find the tension in the rope.

A. Force approach B. Energy approach C. Momentum approach D. Torque approach E. Angular momentum approach

Answer 1

D. Torque approach:  A large crane lifts a grand piano in a crate from the ground to the top of a tall building. To find the work done by the cane

Work done by the crane= Torque*angle of rotation

Where torque = , and = Force acting on the piano, =Arm length of the crane.

Angle of rotation=  Height of the building)/(Arm length of the crane)

E. Angular momentum approach: A bird hits and sticks in a slowly spinning wheel and we want to find how this affects the motion of the wheel.

As the bird sticks to a wheel, the moment of inertia of the wheel changes due to the mass of the bird. By conservation of angular momentum, , we can find the new angular velocity. (As mass of the wheel increases with the bird, its angular velocity is likely to decrease.)

D.Torque approach: A flywheel is spinning and has nothing acting on it but friction. You know the numerical value for the effect of friction. we want to find how long it will take for the flywheel to come to a stop.

Torque acting on the flywheel due to friction =

This torque will cause a deceleration to the wheel motion which is moving with constant angular velocity(As no other torque is acting on it)

From this relation we can find the time t needed for the wheel stop i.e. .

C. Momentum approach:  A truck hits a stationary car head on, and you are able to estimate their velocities right after they hit. We want to calculate if the truck was initially going over the speed limit.

By conservation of linear momentum, Total linear momentum before collision= total linear momentum after collision

From this equation we can find the initial speed of truck.

A. Force approach: A small block sits motionless on a tilted ramp and remains motionless because of friction. You desire to find the coefficient of friction.

[ On a tilted ramp which is at an angle , the net force acting on a mass m = F=  

As the mass remains stationary F=0. Hence e can find the coefficient of friction () ]

B. Energy approach: A spring-loaded dart gun has a known spring constant and compression distance. We want to calculate the highest that a dart can be shot from this gun.

The potential energy stored in the compressed spring provides the kinetic energy of the dart. For the velocity of a dart to be highest, it needs that there is no other form of energy dissipation except the transformation from potential to kinetic energy.

:A. Force approach: A rocket has a known mass and upward thrust. You desire to find the rocket’s acceleration.

[ upward thrust, F= mass of the rocket * acceleration of rocket ]

C. Momentum approach: A spaceship collides with a small asteroid and we want to find how this affects the speed of the spaceship. No spinning motion occurs.

From conservation of linear momentum before and after the collision we can calculate the final speed of the asteroid.

E. Angular momentum approach: A figure skater is spinning and brings her arms in. You desire to find how fast she is spinning at the end.]

angular momentum is conserved before and after bringing her arms in. From , angular velocity after bringing the arms in can be calculated.

A. Force approach: One end of a diagonal ladder sits on the ground and the other end of the ladder hangs from a vertical rope attached to a crane. Everything remains motionless. You desire to find the tension in the rope.

As the ladder hangs from a vertical rope and is itself vertical, tension of the rope (T) = gravitational force on the ladder (m*g)