Motion, forces and energy：練習題

A person puts on snowshoes to walk across deep, soft snow. Which statement correctly explains why the person sinks less into the snow when wearing snowshoes?

A rectangular block with a weight of \(60\text{ N}\) rests on a flat floor. The base of the block has dimensions of \(0.2\text{ m}\) by \(0.5\text{ m}\).

What is the pressure exerted by the block on the floor?

An elephant of mass \( 4000\text{ kg} \) stands on one foot. The area of the base of the foot is \( 0.25\text{ m}^2 \).

Taking \( g = 9.8\text{ N/kg} \), what is the pressure exerted on the ground by the elephant?

A sprinter runs a total distance of \(200\text{ m}\) in a time of \(25\text{ s}\).

What is the sprinter's average speed?

A crane lifts a load of \(2000\text{ N}\) vertically through a height of \(10\text{ m}\).

How much work is done by the crane on the load?

Define the term density and state the formula used to calculate it for a given substance.

A solid block has a mass of \( 450\text{ g} \) and a volume of \( 150\text{ cm}^3 \). Calculate the density (\( \rho \)) of the block and determine if it will sink or float in a liquid with a density of \( 1.2\text{ g/cm}^3 \).

The diagram shows a speed–time graph of a cyclist. The cyclist accelerates uniformly from rest to \( 8\text{ m/s} \) in \( 4\text{ s} \), then travels at this constant speed for \( 6\text{ s} \), and finally decelerates to a stop at a constant rate over \( 2\text{ s} \).

Calculate the total distance travelled by the cyclist by calculating the area under the graph.

An astronaut has a mass of \(75\text{ kg}\). The gravitational field strength on Earth is approximately \(9.8\text{ N/kg}\).

(a) State the difference between mass and weight.
(b) Calculate the weight of the astronaut on Earth.
(c) The astronaut travels to a planet where the gravitational field strength is \(3.7\text{ N/kg}\). Calculate the astronaut's weight on this planet.

A car of mass \( 1200\text{ kg} \) is travelling at a constant speed of \( 15\text{ m/s} \). The driver sees a hazard and applies the brakes, bringing the car to a stop in a distance of \( 30\text{ m} \).

(a) Calculate the initial kinetic energy of the car.
(b) State the amount of work done by the brakes to stop the car, assuming no other energy losses.
(c) Calculate the average braking force applied to the car.