A 10 m long frictionless ramp is inclined at an angle of 30 degress to the horizontal. A boy of mass 57 kg coasts down the incline on a skateboard of mass 3.0 kg. The acceleration due to gravity may be taken as 9.8 m/s^2 and the effects of air resistance can be ignored. a) Calculate the magnitude of the normal force acting on the skateboard and rider. b) what is the resultant force acting parallel to the ramp on board plus rider. c)what is the accelration of the boy down the ramp?

a)mg*CosTheta

b) forceparallel=mg*sinTheta
c) resultant force=mass*acceleration.

No friction force is present.

To solve this problem, we need to break it down into multiple steps. First, let's calculate the magnitude of the normal force acting on the skateboard and rider (part a).

a) The normal force is the force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface. In this case, the normal force is the force exerted by the ramp on the skateboard and rider. Since the ramp is inclined, the normal force will be less than the weight of the skateboard and rider.

To calculate the magnitude of the normal force, we can use the following equation:

Normal force (N) = Weight (W) * cos(θ)

Where:
Weight (W) = mass (m) * acceleration due to gravity (g)
θ = angle of the ramp with respect to the horizontal

Given:
Mass of the boy (m) = 57 kg
Acceleration due to gravity (g) = 9.8 m/s^2
Angle of the ramp (θ) = 30 degrees

First, calculate the weight (W) of the boy and skateboard:

Weight (W) = 57 kg * 9.8 m/s^2 = 558.6 N

Now, calculate the magnitude of the normal force:

Normal force (N) = 558.6 N * cos(30 degrees)

Using a calculator, we can find:

cos(30 degrees) ≈ 0.866

Normal force (N) = 558.6 N * 0.866 ≈ 483.17 N

Therefore, the magnitude of the normal force acting on the skateboard and rider is approximately 483.17 N.

b) The resultant force acting parallel to the ramp on the board plus the rider is calculated as the difference between the applied force (due to gravity) and the force of friction.

Resultant force (F) = Applied force (F_applied) - Force of friction (F_friction)

The applied force is simply the weight of the skateboard and rider:

Applied force (F_applied) = 558.6 N

To calculate the force of friction, we need to know the coefficient of friction (μ). However, since it is not provided in the question and we are told the ramp is frictionless, we can assume there is no force of friction acting on the skateboard and rider. Therefore, the force of friction is zero.

Resultant force (F) = 558.6 N - 0 N = 558.6 N

Therefore, the resultant force acting parallel to the ramp on the board plus the rider is 558.6 N.

c) To calculate the acceleration of the boy down the ramp (part c), we'll use Newton's second law of motion:

Force (F) = mass (m) * acceleration (a)

We already know the resultant force (F) acting parallel to the ramp is 558.6 N, and the combined mass of the boy and the skateboard is given as 57 kg + 3.0 kg = 60 kg.

Substituting these values into the equation, we have:

558.6 N = 60 kg * acceleration (a)

Now, solving for acceleration (a):

acceleration (a) = 558.6 N / 60 kg

Using a calculator, we find:

acceleration (a) ≈ 9.31 m/s^2

Therefore, the acceleration of the boy down the ramp is approximately 9.31 m/s^2.