6. Two blocks are released from rest at the same height. Block A slides down a steeper ramp than Block B. Both ramps are frictionless. The blocks reach the same final height indicated by the lower dashed line. Block B weighs more than Block A. a. Is the work done by the gravitational force on Block A (greater/less than/equal to) the work done by the gravitational force on Block B? Explain your reasoning.
b. Is the speed of Block A (greater/less than/equal to) the speed of Block B? Explain your reasoning.
c. Is the momentum of Block A (greater/less than/equal to) the momentum of Block B? Explain your reasoning.
Answers
Answer:
a. the work done by the gravitational force on Block A is less than the work done by the gravitational force on Block B.
b. the speed of Block A is equal to the speed of Block B.
c. the momentum of Block A is less than the momentum of Block B.
Explanation:
a. The work done by the gravitational force is equal to:
w = m*g*h
where m is mass, g is the standard gravitational acceleration and h is height. Given that both blocks are released from rest at the same height, then, the bigger the mass, the bigger the work done.
b. With ramps frictionless, the final speed of the blocs is:
v = √(2*g*h)
which is independent of the mass of the blocks.
c. The momentum is calculated as follows:
momentum = m*v
Given that both bocks has the same speed, then, the bigger the mass, the bigger the momentum.
Final answer:
The work done by gravitational force on blocks A and B is equal as the work is independent of the path. Both blocks have the same speed when they reach the final height due to the conversion of potential energy into kinetic energy. However, the momentum of Block B is greater due to its larger mass.
Explanation:
This question is about the principles of work, energy and momentum in physics. Let's address each part of it:
- Work done by gravitational force: The work done by the gravitational force on both blocks A and B is equal. This is because work done by gravity depends only on the change in height, which is the same for both blocks, and the weight of the block. So, even though Block B is heavier as it weighs more than Block A, the work done is the same because the force of gravity has to move the blocks the same vertical distance.
- Speed of the blocks: The speed of both blocks A and B will be equal when they reach the final height. This is because, in the absence of friction and air resistance, the blocks will convert all of their gravitational potential energy at the start into kinetic energy at the end, irrespective of their weights or the steepness of the ramps.
- Momentum of the blocks: The momentum of Block B is greater than Block A. This is because momentum depends on both the mass and the velocity of an object. Even though both blocks have the same speed at the bottom, Block B is heavier, therefore, it will have more momentum.
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Answers
Answer:
D, it would decrease by a factor of 4
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ii) The block starts at rest from a height of 8m above the ground. What is the speed of the block when it reaches the bottom of the incline.
Answers
Answer:
Acceleration = 2.35 m/
Speed = 8.67 m/s
Explanation:
The coefficient of friction , u =0.3
The angle of incline = 30°
The two forces acting on block are weight and friction.
weight along the incline = mg cos60° = = 0.5 mg
Friction along incline = umg cos30° = mg
Friction along incline = 0.26 mg
Net force acting on the weight = (0.5 - 0.26) mg = 0.24 mg
Acceleration = = 0.24 g = 2.35 m/
The height of incline = 8 m
Length of the inclined edge = 16 m
v= 8.67 m/s