An trunk weighing 518 N is resting on a plane inclined 25° above the horizontal.
(a) Calculate the magnitude of the acceleration of the trunk (ignore friction).
(b) After 6.00 s, how fast would the trunk be moving?
To solve this problem, we need to break it down into two parts.
(a) First, let's calculate the magnitude of the acceleration of the trunk. We can do this by analyzing the forces acting on the trunk.
The force acting downward is the weight of the trunk, which can be calculated using the formula:
Weight = mass * acceleration due to gravity
Given that the weight of the trunk is 518 N, we can rewrite this formula as:
518 N = mass * 9.8 m/s^2
Now, let's find the mass of the trunk:
mass = weight / acceleration due to gravity
mass = 518 N / 9.8 m/s^2
Once we have the mass of the trunk, we can use Newton's second law of motion:
Force = mass * acceleration
Since we're considering only the component of the weight acting parallel to the incline, the force can be calculated as:
Force = weight * sin(angle of inclination)
Substituting the known values, we get:
Force = 518 N * sin(25°)
Now, we know that force = mass * acceleration, so we can rearrange the formula to solve for acceleration:
acceleration = Force / mass
Substituting the known values, we get:
acceleration = (518 N * sin(25°)) / (518 N / 9.8 m/s^2)
Simplifying further, we find:
acceleration = sin(25°) * 9.8 m/s^2
Therefore, the magnitude of the acceleration of the trunk is sin(25°) * 9.8 m/s^2, which can be calculated using a calculator.
(b) To find out how fast the trunk would be moving after 6.00 s, we can use the equation of motion:
final velocity = initial velocity + (acceleration * time)
Since the trunk is initially at rest (initial velocity = 0), the equation simplifies to:
final velocity = acceleration * time
Substituting the known values, we get:
final velocity = (sin(25°) * 9.8 m/s^2) * 6.00 s
Simplifying further, we find:
final velocity = sin(25°) * 9.8 m/s^2 * 6.00 s
Therefore, the final velocity of the trunk after 6.00 s is sin(25°) * 9.8 m/s^2 * 6.00 s, which can be calculated using a calculator.
a. Fp = 518*sin25 = 218.9 N. = Force
parallel to the incline.
m*g = 518 N.
m = 518/g = 518/9.8 = 52.86 kg.
a = F/m = 218.9/52.86 = 4.14 m/s^2.
b. V = Vo + a*t = 0 + 4.14*6=24.85 m/s.