Calculate Acceleration, Friction & Speed on 30° Incline | Block Homework

In summary, the problem involves a 3.00-kg block sliding down a 30.0° incline for a distance of 2.00 m in 1.50 s. The goal is to find the (a) magnitude of the acceleration, (b) coefficient of kinetic friction, (c) friction force, and (d) final speed of the block after sliding 2.00 m. The equations used are a = 1.78 m/s^2 and Uk = (a + gsin@)/gcos@, and the mistake in the calculations was due to incorrect signs in the equations. After correcting the signs, the correct values can be obtained.
  • #1
Ab17
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Homework Statement


3.00-kg block starts from rest at the top of a 30.0° incline and slides a distance of 2.00 m down the incline in 1.50 s. Find (a) the magnitude of the acceler- ation of the block, (b) the coefficient of kinetic friction between block and plane, (c) the friction force acting on the block, and (d) the speed of the block after it has slid 2.00 m.

Homework Equations

The Attempt at a Solution


a = 1.78 m.s2

(B) fk - mgsin@ = ma
Ukmgcos@ - mgsin@ = ma
Ukgcos@ -gsin@ = a
Uk= (a+ gsin@)/gcos@
Uk = 0.787
 
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  • #2
Not getting the correct answer where am I going wrong?
 
  • #3
You have a sign issue with the directions of the vector components. Draw an FBD that shows the directions of the vectors involved. Include the acceleration vector so that your choice of coordinate system is clear (so that the signs you assign to the force vectors when you write your equations match your choice of + direction for the acceleration).
 
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  • #4
Oh yes its suppost to be mgsin@ -fk
 
  • #5
But i still get the same eqn
 
  • #6
Ab17 said:
But i still get the same eqn
Signs should change in your equation.
 
  • #7
Ya I see it now. I made such a stupid mistake
 

FAQ: Calculate Acceleration, Friction & Speed on 30° Incline | Block Homework

1. What is acceleration and how do you calculate it?

Acceleration is the rate of change of an object's velocity. It is calculated by dividing the change in velocity by the change in time. The formula for acceleration is: a = (vf - vi) / t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

2. How do you calculate friction on a 30° incline?

To calculate friction on a 30° incline, you will need to know the mass of the object, the coefficient of friction, and the angle of the incline. The formula for friction on an incline is: Ff = μmgcosθ, where Ff is the force of friction, μ is the coefficient of friction, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s²), and θ is the angle of the incline.

3. What is the formula for finding speed on a 30° incline?

The formula for finding speed on a 30° incline is: v = √(2ghsinθ), where v is the speed, g is the acceleration due to gravity (9.8 m/s²), h is the height of the incline, and θ is the angle of the incline.

4. How can I use the equations for acceleration, friction, and speed to solve a block homework problem?

To solve a block homework problem, you will need to identify the given variables and use the appropriate equations to calculate the unknown variable. Start by drawing a diagram and labeling the known values. Then, choose the equation that relates the known and unknown values and solve for the unknown variable.

5. Can you provide an example problem using these equations?

Sure! Let's say a block with a mass of 5 kg is placed on a 30° incline. The coefficient of friction between the block and the incline is 0.2. The block is initially at rest and slides down the incline for 5 seconds. What is the block's final speed?

First, we need to calculate the force of friction on the block. Using the formula, Ff = μmgcosθ, we get: Ff = (0.2)(5 kg)(9.8 m/s²)cos(30°) = 9.8 N. Next, we can use the formula for acceleration, a = (vf - vi) / t, to solve for the final velocity. Since the block starts at rest, the initial velocity (vi) is 0. Plugging in the known values, we get: a = (vf - 0) / 5 s. Solving for vf, we get: vf = 5 m/s. Therefore, the block's final speed after 5 seconds is 5 m/s down the incline.

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