A mass on a frictinless inclined ramp is connected to a rope with tension T. Complete the senteces with correct selection:
-increases
-decreases
-stays the same
a) If the block is moving up the ramp and theta=30 deg, its speed initally _________ if T=(mg)/2
b) If the block is moving down the ramp and theta is more than 30 deg, its speed initally _________ if T=(mg)/2
c) If the block is moving up the ramp at increasing spped, T is ______ the normal foce of the ramp on the block.
Thank you so much in advance!
I am not going to do this for you. I will be happy to critique your thinking.
This is what i reasoned:
a) if block is moving up the ramp, it means that tension is greater than the sin of mg. if T was half of mg, that means the speed decreases up the ramp because the T force is less.
b) it would increase. i don't understand what the 30 deg has to do with anything, i suppose if i had actual values it would make a difference in the force pulling the mass down... but T is still half of the force pulling the weight down.
c) i suppose it stays the same, because the normal force is the same as sin of theta, which does not effect the horizontal values to the ramp.
im sorry that's a lot to read, does it sound right?
a) Look at the component of weight down the plane: mg*sinTheta= mg/2
if tension is that, the block is at constant velocity , as net force up plane is T-mg/2.
b) if net force is T-mgsinTheta, and theta is greater than 30, the net force is negative, or down the ramp. So it speeds up down the ramp.
c)The question makes no sense. If it is going up the ramp, T is > mgsinTheta, or T is greater than the down the ramp component of weight. Normal force is not in the picture, as it is frictionless. At 45 deg, Normal= down plane force. At greater than 45, down the slope is > normal force, and below 45, normal is greater than down the slope. The question does not make sense.
Your instructor could have done a better job of measuring reasoning on this.
thank you SO much, i got them all right in the first try! the answer to question c is "need more information"
a) If the block is moving up the ramp and theta = 30 degrees, its speed initially __stays the same__ if T = (mg)/2.
To understand why the speed stays the same, we can consider the forces acting on the block. The tension force T is acting upwards along the ramp, while the gravitational force mg is acting downwards. Since the incline is frictionless, there is no horizontal force. Therefore, these two forces are the only ones affecting the motion of the block.
By using trigonometry, we can find that the vertical component of the gravitational force is (mg)sin(30), and it is equal to T since the block is in equilibrium. The horizontal component of the gravitational force is (mg)cos(30), which doesn't affect the motion of the block along the incline.
Since the vertical component of the gravitational force is balanced by the tension force T, the net force acting on the block is zero. According to Newton's second law, F = ma, where F is the net force and a is the acceleration. Since the net force is zero, the acceleration is also zero. Therefore, the speed of the block initially stays the same.
b) If the block is moving down the ramp and theta is more than 30 degrees, its speed initially __decreases__ if T = (mg)/2.
To understand why the speed decreases, we can consider the forces acting on the block. The tension force T is acting downwards along the ramp, while the gravitational force mg is acting downwards as well. Since the incline is frictionless, there is no horizontal force. Therefore, these two forces are the only ones affecting the motion of the block.
By using trigonometry, we can find that the vertical component of the gravitational force is (mg)sin(theta), and it is greater than T since the block is moving downwards. The horizontal component of the gravitational force is (mg)cos(theta), which doesn't affect the motion of the block along the incline.
Since the vertical component of the gravitational force is larger than the tension force T, there is a net force acting downwards on the block. According to Newton's second law, F = ma, where F is the net force and a is the acceleration. Since the net force is downwards, the acceleration is negative, causing the speed of the block to decrease.
c) If the block is moving up the ramp at increasing speed, T is __increases__ the normal force of the ramp on the block.
To understand why T increases the normal force, we need to consider the forces acting on the block. The tension force T is acting upwards along the ramp, while the gravitational force mg is acting downwards. Since the block is moving upwards at increasing speed, there must be a net force acting upwards.
The net force is the vector sum of the tension force T and the vertical component of the gravitational force (mg)sin(theta). If the speed of the block is increasing, the magnitude of the net force must be larger than the magnitude of the force of gravity. Therefore, T must be greater than (mg)sin(theta).
The normal force on the block is equal to the vertical component of the gravitational force, which is (mg)cos(theta). Since (mg)cos(theta) is less than T, the tension force, T, is greater than the normal force.
Note: It's important to keep track of the signs of the forces while considering their direction along the inclined ramp.