What is the correct force to accelerate a block on an incline?

[nokia8650]

I am struggling with the following problem:

http://img50.imageshack.us/img50/2682/img184yj5.th.jpg http://g.imageshack.us/thpix.php

http://img407.imageshack.us/img407/9342/img182et8.th.jpg

I have found that the resultant force on the block must be 500N, and therefore the force supplied must be 1500N. However, I then get a ratio of 30 for the area - the correct answer is 10 in the back of the book.

Thanks for any help in advance

 

[Redbelly98]

Hmmm ... your answer makes sense to me. It's as if they forgot to include the block's weight in the calculation.

(This would be an unwieldy method for accelerating the block anyway, since the device would have to be at least 250m high.)

 

[baba89]

The correct force to accelerate a block on an incline can be determined by using Newton's Second Law, which states that the force applied to an object is equal to its mass multiplied by its acceleration (F=ma). In this case, we can use the force of gravity (weight) acting on the block as the force applied. The weight of the block can be calculated by multiplying its mass (m) by the acceleration due to gravity (g=9.8 m/s^2).

Next, we need to consider the forces acting on the block in the direction of motion. These forces include the weight of the block (acting downwards), the normal force (acting perpendicular to the incline), and the force of friction (acting parallel to the incline). In order for the block to accelerate, the resultant force in the direction of motion must be greater than the force of friction.

Using the information provided in the problem, we can set up the following equation:

F - Ff = ma

Where F is the force applied (weight), Ff is the force of friction, m is the mass of the block, and a is the acceleration.

We can also use the relationship between the angle of the incline and the force of friction, given by:

Ff = μN

Where μ is the coefficient of friction and N is the normal force.

Substituting μN for Ff in the first equation, we get:

F - μN = ma

Now, we can solve for the force applied (F) by rearranging the equation:

F = ma + μN

We know the mass of the block (m=50kg) and the acceleration (a=3 m/s^2), so we just need to find the normal force (N) and the coefficient of friction (μ).

To find the normal force, we can use trigonometry and the angle of the incline given in the problem (θ=30°):

N = mgcosθ

= (50kg)(9.8 m/s^2)cos30°

= 490N

To find the coefficient of friction, we can use the information given in the problem that the block is just about to slide:

μ = tanθ

= tan30°

= 0.577

Now, we can plug these values into our equation for F:

F = (50kg)(3 m/s^2) + (0.577)(490N)