The 10 kg mass is released from rest at a height of 1m above the floor. If the co-efficient of kinetic friction between the 5 kg mass and the table is 0.28, what will be the speed of the 10 kg mass just before it hits the floor?
Please show the equation and then plug the numbers into that equation
V^2 = Vo^2 + 2g*h.
V^2 = 0 + 19.6*1 =
So the answer is 19.6 m/s right?
V^2 = 19.6, V = 4.43 m/s.
To determine the speed of the 10 kg mass just before it hits the floor, we can use the principle of conservation of mechanical energy.
First, let's calculate the potential energy of the 10 kg mass when it is at a height of 1m above the floor. The potential energy is given by the equation:
PE = mgh
where m is the mass (10 kg), g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height (1 m). Plugging in the given values, we have:
PE = 10 kg * 9.8 m/s² * 1 m
= 98 J
Next, let's take into account the work done against friction as the 10 kg mass slides down. The work done by friction is given by:
W = f * d
where f is the frictional force and d is the distance. The frictional force can be calculated using the equation:
f = μ * N
where μ is the coefficient of kinetic friction (0.28) and N is the normal force. The normal force can be calculated by considering the weight of the 5 kg object on the table as it accelerates:
N = m * g
where m is the mass (5 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²). Plugging in the given values, we have:
N = 5 kg * 9.8 m/s²
= 49 N
Now we can calculate the frictional force:
f = 0.28 * 49 N
= 13.72 N
Since the 10 kg mass slides down a distance of 1 m, the work done against friction is given by:
W = f * d
= 13.72 N * 1 m
= 13.72 J
Now, let's use the principle of conservation of mechanical energy. The total mechanical energy at the top (potential energy) is equal to the total mechanical energy at the bottom (kinetic energy). Therefore, we can equate the initial potential energy to the final kinetic energy:
PE = KE
Where KE is the kinetic energy, given by:
KE = 0.5 * m * v²
Where m is the mass (10 kg) and v is the final velocity we want to find.
Substituting the values, we have:
98 J = 0.5 * 10 kg * v²
98 J = 5 kg * v²
19.6 J = v²
v² = 19.6 J
Now, to obtain the velocity v, we can take the square root of both sides:
v = √(19.6 J)
v ≈ 4.43 m/s
So, the speed of the 10 kg mass just before it hits the floor will be approximately 4.43 m/s.