7.4 Power

Estimate the power expended by a weightlifter raising a 150-kg barbell 2 m in 3 s.

Most electrical appliances are rated in watts. Does this rating depend on how long the appliance is on? (When off, it is a zero-watt device.) Explain in terms of the definition of power.

A spark of static electricity, such as that you might receive from a doorknob on a cold dry day, may carry a few hundred watts of power. Explain why you are not injured by such a spark.

Can the power expended by a force be negative?

A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people would it take to run a 4.00-kW electric clothes dryer? (b) How many people would it take to replace a large elec…

A large household air conditioner may consume 15.0 kW of power. What is the cost of operating this air conditioner 3.00 h per day for 30.0 d if the cost of electricity is $0.110 per $\text{kW} \cdot \text{h}$?

(a) What is the average useful power output of a person who does $6.00 \times 10^{6} \text{J}$ of useful work in 8.00 h? (b) Working at this rate, how long will it take this person to lift 2000 kg of bricks 1.50 m to a platform? (Work done to lift his body can be omitted because it is not considered useful output here.)

(a) How long will it take an 850-kg car with a useful power output of 40.0 hp (1 hp equals 746 W) to reach a speed of 15.0 m/s, neglecting friction? (b) How long will this acceleration take if the car also climbs a 3.00-m high hill in the process?

(a) How long would it take a $1.50 \times 10^{5} -\text{kg}$ airplane with engines that produce 100 MW of power to reach a speed of 250 m/s and an altitude of 12.0 km if air resistance were negligible? (b) If it actually takes 900 s, what is the power? (c) Given this power, what is the average force of air resistance if the airplane takes 1200 s? (Hint: You must find the distance the plane travels in 1200 s assuming constant a…

A man of mass 80 kg runs up a flight of stairs 20 m high in 10 s. (a) how much power is used to lift the man? (b) If the man’s body is 25% efficient, how much power does he expend?

An electron in a television tube is accelerated uniformly from rest to a speed of $8.4 \times 10^{7} \text{m}/\text{s}$ over a distance of 2.5 cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?

A girl pulls her 15-kg wagon along a flat sidewalk by applying a 10-N force at $37 °$ to the horizontal. Assume that friction is negligible and that the wagon starts from rest. (a) How much work does the girl do on the wagon in the first 2.0 s. (b) How much instantaneous power does she exert at $t = 2.0 \text{s}$?

When jogging at 13 km/h on a level surface, a 70-kg man uses energy at a rate of approximately 850 W. Using the facts that the “human engine” is approximately 25% efficient, determine the rate at which this man uses energy when jogging up a $5.0 °$ slope at this same speed. Assume that the frictional retarding force is the same in both cases.

Consider a particle on which several forces act, one of which is known to be constant in time: $\overset{\rightarrow}{F}_{1} = \left(3 \text{N}\right) \hat{i} + \left(4 \text{N}\right) \hat{j} .$ As a result, the particle moves along the x-axis from $x = 0$ to $x = 5 \text{m}$ in some time interval. What is the work done by $\overset{\rightarrow}{F}_{1}$ ?

Consider a particle on which several forces act, one of which is known to be constant in time: $\overset{\rightarrow}{F}_{1} = \left(3 \text{N}\right) \hat{i} + \left(4 \text{N}\right) \hat{j} .$ As a result, the particle moves along a straight path from a Cartesian coordinate of (0 m, 0 m) to (5 m, 6 m). What is the work done by $\overset{\rightarrow}{F}_{1}$ ?

A boy pulls a 5-kg cart with a 20-N force at an angle of $30 °$ above the horizontal for a length of time. Over this time frame, the cart moves a distance of 12 m on the horizontal floor. (a) Find the work done on the cart by the boy. (b) What will be the work done by the boy if he pulled with the same force horizontally instead of at an angle of $30 °$ above the horizontal over the same distance?

A hockey puck of mass 0.17 kg is shot across a rough floor with the roughness different at different places, which can be described by a position-dependent coefficient of kinetic friction. For a puck moving along the x-axis, the coefficient of kinetic friction is the following function of x, where x is in m: $\mu \left(x\right) = 0.1 + 0.05 x .$ Find the work done by the kinetic frictional force on the hockey puck when it has moved…

A 7.0-kg box slides along a horizontal frictionless floor at 1.7 m/s and collides with a relatively massless spring that compresses 23 cm before the box comes to a stop. (a) How much kinetic energy does the box have before it collides with the spring? (b) Calculate the work done by the spring. (c) Determine the spring constant of the spring.

A crate is being pushed across a rough floor surface. If no force is applied on the crate, the crate will slow down and come to a stop. If the crate of mass 50 kg moving at speed 8 m/s comes to rest in 10 seconds, what is the rate at which the frictional force on the crate takes energy away from the crate?

Grains from a hopper falls at a rate of 10 kg/s vertically onto a conveyor belt that is moving horizontally at a constant speed of 2 m/s. (a) What force is needed to keep the conveyor belt moving at the constant velocity? (b) What is the minimum power of the motor driving the conveyor belt?

Answer the preceding problem using polar coordinates.

Answer the preceding problem using polar coordinates.

Suppose that the air resistance a car encounters is independent of its speed. When the car travels at 15 m/s, its engine delivers 20 hp to its wheels. (a) What is the power delivered to the wheels when the car travels at 30 m/s? (b) How much energy does the car use in covering 10 km at 15 m/s? At 30 m/s? Assume that the engine is 25% efficient. (c) Answer the same questions if the force of air res…