Question

a conveyor belt ramp of length is inclined at with respect to the horizontal and is used to move objects from one location to another location. when an object is placed on the conveyor belt, the object travels up the incline with a constant speed of . a motor is used to keep the conveyor belt moving. the mass of the objects that are placed on the conveyor belt are varied. question suppose the motor breaks and a person must push an object of mass from the bottom of the incline to the top of the incline. the person can exert a force of on the object parallel to the incline. what is the approximate amount of work that the person does on the object to move it to the top of the incline? assume that all frictional forces are negligible. responses 0 joule 1050 joules 658 joules

Answer 1

The amount of work that the person does on the object to move it to the top of the incline is 988.275 J.

The work done by the person to move the object up the incline is given by the formula:

`\[ \text{Work} = \text{Force} * \text{Distance} * \cos(\theta) \]`

where:

• Force is the force applied by the person (150 N),
• Distance is the length of the incline (7 m),
• 
  `\( \theta \)` is the angle of the incline (20 degrees).

Let's calculate by substituting the various variables:

`\[ \text{Work} = 150 \, \text{N} * 7 \, \text{m} * \cos(20^\circ) \]`

Cos
`20^o` = 0.9397

Thus:

`\[ \text{Work} \approx 150 \, \text{N} * 7 \, \text{m} * 0.9397 \]`

`\[ \text{Work} \approx 988.275 \, \text{J} \]`

Therefore, the approximate amount of work that the person does on the object to move it to the top of the incline is 988.275 J.

The complete question:

A conveyor belt ramp of length 7m is inclined at 20° with respect to the horizontal and is used to move objects from one location to another location. When an object is placed on the conveyor belt, the object travels up the incline with a constant speed of 1.5 m/s . A motor is used to keep the conveyor belt moving. The mass of the objects that are placed on the conveyor belt are varied. Suppose the motor breaks and a person must push an object of mass 30kg from the bottom of the incline to the top of the incline. The person can exert a force of 150N on the object parallel to the incline. What is the approximate amount of work that the person does on the object to move it to the top of the incline? Assume that all frictional forces are negligible.