Question

A block of stone weighs 500 newtons. It is 20m pushed up a slope. (a) Neglecting friction, how much force is needed to push it up the incline at constant velocity? (b)(i) How much work is done to push it up the incline?

(i) How much work is done in lifting the block vertically 4m ?

Answer 1

The force to push a 500 N block up an incline at constant speed is equal to the gravitational parallel component which depends on the incline angle.

The work done is the force times the distance moved, and lifting the block 4m vertically involves 2000 joules of work.

Step-by-step explanation:

The question concerns the application of classical mechanics to calculate the work done and forces involved when moving an object along an incline. Specifically, the task is to determine:

1. The force needed to push a block of stone weighing 500 newtons up a slope at constant velocity, neglecting friction.
2. The work done to push it up the incline.
3. The work done in lifting the block vertically for a given distance.

(a) When pushing an object up an incline at a constant velocity and neglecting friction, the force needed will be equal to the component of the weight of the block that is parallel to the slope. This is calculated based on the angle of the incline, which isn't provided in the question. However, if the incline creates an angle such that the only force required is to counteract the object's weight parallel to the slope, then the force required would equal gravity's pull down the slope.

(b)(i) Work done is the product of the force applied and the distance moved in the direction of the force. In this case, work done to push it up the incline would be force multiplied by the distance (20 meters), but the actual value cannot be determined without knowing the angle of the incline and the corresponding parallel force component.

(ii) The work done in lifting the block vertically 4m is torque calculated by the weight of the object (force due to gravity) multiplied by the vertical distance lifted, which in this case is 500 N × 4 m = 2000 joules.

Answer 2

(a) The force needed to push the block up the incline at constant velocity can be calculated using Newton's second law of motion, F = m * a, where m is the mass of the block and a is the acceleration. Neglecting friction, the acceleration is 0, so the force needed is also 0.

(b)(i) The work done to push the block up the incline is equal to the force required to push the block multiplied by the distance it is moved, W = F * d. Since the force required is 0 (as calculated in (a)), the work done is also 0.

(ii) The work done in lifting the block vertically 4m can be calculated as W = F * d, where F is the force required to lift the block and d is the distance it is lifted. The force required is equal to the weight of the block, F = m * g = 500 N, where g is the acceleration due to gravity (9.8 m/s^2). The work done is W = F * d = 500 N * 4 m = 2000 J (joules).