A wet bar of soap slides freely down a ramp 2.0 m long inclined at 6.8o. How long does it take to reach the bottom? Neglect friction.
force down the plane: mg*sinTheta.
F=ma solve for a, then...
Vf^2=2ad
Thank you.... :-)
bt how do u find the mass......the mass is not given in the question
To find the time it takes for the wet bar of soap to slide down the ramp without considering friction, you can use the principles of physics, specifically kinematics.
First, let's break down the problem:
Given:
- Length of the ramp, L = 2.0 m
- Incline angle of the ramp, θ = 6.8°
- Neglecting friction
Now, let's consider the motion of the soap bar along the ramp.
1. Resolve the gravitational force:
The gravitational force acting on the soap bar can be resolved into two components: perpendicular to the ramp (mg⋅cosθ) and parallel to the ramp (mg⋅sinθ), where m is the mass of the soap bar and g is the acceleration due to gravity.
2. Acceleration along the ramp:
Since there is no friction, the component of the gravitational force parallel to the ramp (mg⋅sinθ) is the only force accelerating the soap bar along the ramp. Therefore, the acceleration along the ramp, a, can be calculated using the formula: a = g⋅sinθ.
3. Equation of motion:
We can use the equation of motion for uniformly accelerated linear motion: s = ut + (1/2)at², where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration.
In this case, the distance traveled, s, is equal to the length of the ramp, L.
Since the initial velocity, u, is zero (since the soap bar starts at rest), the equation simplifies to: L = (1/2)at².
4. Solve for time:
Rearrange the equation to solve for time, t: t = √(2L/a).
Now, plug in the known values into the equation:
L = 2.0 m
θ = 6.8°
g = 9.8 m/s² (acceleration due to gravity)
Calculate the acceleration, a, by multiplying g by sinθ:
a = 9.8 m/s² * sin(6.8°)
Now, substitute the values of L and a into the equation:
t = √(2 * 2.0 m) / a
Finally, calculate the time, t.
Note: Make sure to convert the angle to radians before calculating the sine function.
When you substitute the values and solve the equation, you will get the time it takes for the wet bar of soap to reach the bottom of the ramp without considering friction.