13.5.A.1Multiple Choice
Two identical lamps each convert 100 J of electrical energy into light and heat. Lamp A does this over 2 s; Lamp B does this over 4 s. Which statement is correct?
Select A, B, C, or D to check your answer.
Directions:Work each problem on your own paper first. For multiple choice, select A, B, C, or D. You will see right away whether you are correct. If you miss, you will see the most likely reason, and you can try again. For short response, type your answer, then compare it with the model solution. Questions mix the five essential knowledge threads of Topic 3.5 — what power means as a rate rather than an amount, average power from energy transferred or converted, average power from work done, instantaneous power as dW/dt (including reading W-t and P-t graphs), and instantaneous power from a constant force, P = Fv cosθ. Use g = 10 m/s² unless a problem gives you other values to use. Round decimals to the nearest tenth unless noted otherwise.
Two identical lamps each convert 100 J of electrical energy into light and heat. Lamp A does this over 2 s; Lamp B does this over 4 s. Which statement is correct?
Select A, B, C, or D to check your answer.
A hair dryer transfers 36,000 J of electrical energy from the wall outlet into the dryer–air system (a transfer across the system's boundary) over 30 s of operation. Inside the dryer, that electrical energy is converted into thermal energy that warms the air (a conversion within the system). (a) Identify which part of this scenario is a transfer and which part is a conversion. (b) Find the average power.
Which of the following is an example of energy conversion within a system, rather than a transfer across its boundary?
Select A, B, C, or D to check your answer.
A pole vaulter converts 2400 J of kinetic energy into elastic potential energy stored in a bending pole over a 0.6 s plant-and-bend, and that elastic PE then converts into gravitational PE as the vaulter rises. (a) Identify how many distinct energy conversions are described here. (b) Find the average power of the first conversion. (c) Explain why this entire multi-step process can still be described using Pavg = ΔE/Δt.
A heater transfers 90,000 J of energy into a room over 1 minute. What is the average power of the heater?
Select A, B, C, or D to check your answer.
An electric kettle delivers a total of 180,000 J of energy to the water inside it over 8 minutes. (a) Convert 8 minutes to seconds. (b) Find the average power of the kettle. (c) If the kettle instead took twice as long to transfer the same amount of energy, what would its average power be?
A 2800 W microwave runs for 45 s. How much energy does it transfer to the food?
Select A, B, C, or D to check your answer.
Over a 5 s interval, a system gains 15,000 J of kinetic energy and loses 4000 J of potential energy, with no other energy changes and no nonconservative losses. (a) Find the total change in the system's energy. (b) Find the average power associated with this total change. (c) Explain why the potential energy decreasing doesn't automatically make the total change negative.
A person does 6000 J of work pushing a stalled car over 40 s. What average power does the person deliver?
Select A, B, C, or D to check your answer.
A crane cable does 54,000 J of work lifting a crate at a constant average power of 900 W. (a) Find the time taken for this lift. (b) If the crane instead wanted to lift an identical crate to the same height in half the time, what average power would it need to deliver?
A single force does +3000 J of work on an object over 10 s, while a second force does −1000 J of work on the same object over that same 10 s. What is the average power delivered to the object by the net force?
Select A, B, C, or D to check your answer.
A tractor's engine does 240,000 J of work pulling a plow over 2 minutes, while friction between the plow and soil does −90,000 J of work on the plow over that same time. (a) Find the net work done on the plow. (b) Find the average power delivered by the engine alone. (c) Find the average net power delivered to the plow.
The work done on an object is given by W(t) = 5t² (joules, t in seconds). What is the instantaneous power at t = 3 s?
Select A, B, C, or D to check your answer.
The work done on a system is given by W(t) = 2t³ (joules, t in seconds), for t between 0 and 4 s. (a) Find the instantaneous power Pinst(t) using Pinst = dW/dt. (b) Evaluate the instantaneous power at t = 2 s. (c) Evaluate the instantaneous power at t = 4 s, and state whether the power is increasing or decreasing over this interval.
A P(t) graph shows instantaneous power constant at 40 W from t = 0 to t = 5 s, then constant at 10 W from t = 5 s to t = 15 s. What is the average power over the full 0–15 s interval?
Select A, B, C, or D to check your answer.
A system's instantaneous power is constant at 80 W for the first 3 s, then constant at 20 W for the next 9 s. (a) Find the work done during each segment. (b) Find the total work done over the full 12 s. (c) Find the average power over the full 12 s, and explain why it ends up closer to 20 W than to 80 W.
A constant 500 N force acts on an object in the exact same direction as its velocity, which is 6 m/s at a certain instant. What is the instantaneous power delivered by this force at that instant?
Select A, B, C, or D to check your answer.
A rope pulls a box at a constant 60 N, directed 40° above the horizontal, while the box slides horizontally at 2 m/s. (a) Identify the angle θ to use in Pinst = Fv cosθ. (b) Find the instantaneous power delivered by the rope. (c) Would the power be larger, smaller, or the same if the rope were instead horizontal (0°), still pulling at 60 N, with the box still moving at 2 m/s? Explain.
A constant force is applied to an object exactly perpendicular to the object's velocity at every instant (as in uniform circular motion). What is the instantaneous power delivered by this force?
Select A, B, C, or D to check your answer.
A car's engine exerts a constant net forward force of 2400 N as the car accelerates from rest in a straight line, with the force parallel to the velocity throughout. A graph of the instantaneous power delivered by this force shows it rising linearly from 0 W at t = 0 s to 36,000 W at t = 15 s. (a) Find the car's speed at t = 15 s using Pinst = Fv. (b) Find its speed at t = 7.5 s, where the graph shows P ≈ 18,000 W. (c) Based on your answers to (a) and (b), determine whether the car's acceleration is constant over this interval, and explain how you can tell directly from a P(t) graph that is a straight line through the origin.