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37 problems tagged with work-energy

Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy
Mechanics › Work and Energy

P0533

Beginner Mechanics › Work and Energy

Work Done by Position-Dependent Forces

We move a particle along an x axis, first outward from $x = 1.0$ m to $x = 4.0$ m and then back to $x = 1.0$ m, while an external force acts on it. That force is directed along the x axis, and its x component can have different values for the outward trip and for the return trip. Here are the values (in newtons) for four situations, where x is in meters:

Outward / Inward (a) +3.0 / -3.0 (b) +5.0 / +5.0 (c) +2.0x / -2.0x (d) +3.0x^2 / +3.0x^2

[QUESTIONS] [Q(a-d)] Find the net work done on the particle by the external force for the round trip for each of the four situations. [Q(e)] For which, if any, is the external force conservative? [/QUESTIONS]

calculus work-energy

P0447

Beginner Mechanics › Work and Energy

Work and Friction for a Block Pulled at an Angle

A block of mass $m$ on a horizontal surface is pulled by a force $F$ at an angle $\theta$ above the horizontal. The block moves a distance $d$ at a constant velocity.

  1. How many forces are acting on the block?
  2. Find the work done on the block by each force and the work done by the net force.
  3. Find the coefficient of kinetic friction $\mu_k$ between the block and the surface.
work-energy

P0448

Beginner Mechanics › Work and Energy

Work Done by Angled Force on Horizontal Surface

A person pushes an object with a mass of $m = 3.0$ kg at a constant velocity for a distance of $s = 10$ m across a horizontal floor. The pushing force is directed downwards at an angle of $\theta = 30^\circ$ relative to the displacement. The coefficient of kinetic friction between the object and the floor is $\mu = 0.20$.

Find the work done by the person on the object.
work-energy

P0449

Beginner Mechanics › Work and Energy

Work on a Box Pushed Up an Incline

A horizontal force $F$ is used to push a wooden box of mass $m=50$ kg at a constant velocity up an inclined plane. The plane is inclined at $\theta = 30^\circ$ and the box is pushed for a distance of $s=6.0$ m. The coefficient of kinetic friction between the box and the plane is $\mu = 0.20$.

  1. Find the work done by the pushing force ($W_F$).
  2. Find the work done by the frictional force ($W_f$).
  3. Find the work done by the normal force ($W_N$).
  4. Find the work done by gravity ($W_G$).
  5. Find the work done by the net force ($W_{net}$).
work-energy

P0450

Beginner Mechanics › Work and Energy

Work Sign from a Velocity-Time Graph

Under the action of a single variable force, an object undergoes linear motion. Its velocity-time graph is shown in the figure.

Determine the sign (positive, negative, or zero) of the work done by this force during the time intervals OB, BC, CD, and DE.
work-energy

P0543

Beginner Mechanics › Work and Energy

Kinetic Energy Change on a Frictionless Incline

A block slides a distance $d$ down a frictionless ramp inclined at an angle $\theta$. A rope pulls on the block with a constant force of magnitude $F_r$ directed up the ramp. During this displacement, the block's kinetic energy increases by $\Delta K$.

By how much would the kinetic energy increase have been greater if the rope had not been attached to the block?
work-energy

P0544

Beginner Mechanics › Work and Energy

Work and Energy on a Frictionless Ramp

A book of mass $m$ is pushed by a constant horizontal force $\vec{F_a}$ as it slides a distance $d$ up a frictionless ramp inclined at an angle $\theta$.

  1. Calculate the work done on the book by the applied force ($W_a$), the gravitational force ($W_g$), the normal force ($W_N$), and the net work ($W_{net}$).
  2. If the book starts with zero initial kinetic energy, what is its speed $v_f$ at the end of the displacement?
work-energy

P0545

Beginner Mechanics › Work and Energy

Work and Apparent Weight in an Elevator

A block of cheese of mass $m$ lies on the floor of an elevator cab of mass $M$. The cab is pulled upward by a cable.

  1. Through a distance $d_1$, the normal force on the block from the floor has a constant magnitude $F_{N1}$. How much work $W_{c1}$ is done on the cab by the force from the cable?
  2. Through a distance $d_2$, the work done on the cab by the constant force from the cable is $W_{c2}$. What is the magnitude of the normal force $F_{N2}$ on the block?
work-energy

P0546

Beginner Mechanics › Work and Energy

Work-Energy for a Block Pulled on a Spring

A block lies on a horizontal frictionless surface, attached to a spring with spring constant $k$. Initially, the spring is at its relaxed length and the block is stationary at position $x=0$. Then, a constant applied force of magnitude $F$ pulls the block in the positive $x$ direction, stretching the spring until the block momentarily stops.

  1. What is the position of the block when it stops?
  2. What is the work done on the block by the applied force?
  3. What is the work done on the block by the spring force?
  4. At what position is the block's kinetic energy maximum?
  5. What is the value of the maximum kinetic energy?
work-energy

P0547

Beginner Mechanics › Work and Energy

Work-Energy Theorem with Angled Tension

A cart on a frictionless horizontal rail is pulled by a cord that passes over a pulley. The pulley is at a fixed height $h$ above the rail. The cart moves from an initial position $x_1$ to a final position $x_2$. During the move, the tension $T$ in the cord is constant.

What is the change in the kinetic energy of the cart during the move?
work-energy

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