A 5 kg block sits on a 10 degree incline. There is friction between the block an

Question

A 5 kg block sits on a 10 degree incline. There is friction between the block and the incline.
1. Choose a coordinate system and write out the X and Y components of each force vector.
2. What is the magnitude of the weight vector pointed down the ramp.
3. What is the lowest value for the static coefficient of friction that will keep the block from slipping.
4. What would the static coefficient of friction have to be if the block was 20 kg in mass. A 5 kg block sits on a 10 degree incline. There is friction between the block and the incline.
1. Choose a coordinate system and write out the X and Y components of each force vector.
2. What is the magnitude of the weight vector pointed down the ramp.
3. What is the lowest value for the static coefficient of friction that will keep the block from slipping.
4. What would the static coefficient of friction have to be if the block was 20 kg in mass.
1. Choose a coordinate system and write out the X and Y components of each force vector.
2. What is the magnitude of the weight vector pointed down the ramp.
3. What is the lowest value for the static coefficient of friction that will keep the block from slipping.
4. What would the static coefficient of friction have to be if the block was 20 kg in mass.

Explanation / Answer

1)

let's choose the along the incline plane X-axis and normal to the incline as the Y-axis

then along X-axis

weight vector is m*g*sin(theta) = 5*9.81*sin(10) = 8.52 N along downward along the incline and frictional force along the incline but opposite to 8.52 N

then along Y-axis

m*g*cos(theta) along -Y-axis and NOrmal force N along +Y-axis

2) maginitude of weight vector is m*g*sin(10) = 5*9.81*sin(10) = 8.52 N

3) tan(theta) = mu_s

mu_s = tan(10) = 0.176

4) mu_s = 0.176

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