A person of mass 70kg slides across a slippery floor at 2m/s. If the coefficient of kinetic friction is 0.05 and that of static friction is 0.35.
Find the distance the person will slide before stopping.
I will assume that 2 m/s is the initial speed. It decelerates after that. The deceleration rats is
a = -M*g*uk /M = 0.05*9.8 m/s^2
= -0.049 m/s^2
The static coefficient will not affect the answer.
Sliding distance = (1/2)M Vo^2/(uk*M*g)
(1/2)V^2/(uk*g)
How many possible orientations are there in a bulb, battery, and wire are there that don't result in the bulb lighting? Need four of these as drawings.
You should have posted this as a separate question, not as an addition to a previous thread.
We cannot provide drawings with answers, in any case.
If you are looking for wiring isturations that do NOT work, try leaving out the bulb, the battery, both, and leaving a disconnected wire
To find the distance the person will slide before stopping, we need to consider the forces acting upon the person.
The force of friction opposes the motion of the person and eventually brings them to a stop. There are two types of friction to consider: kinetic friction and static friction.
The force of kinetic friction (Fk) can be calculated using the equation:
Fk = μk * N
where μk is the coefficient of kinetic friction and N is the normal force acting on the person. The normal force in this case is equal to the weight of the person, which can be calculated as:
N = m * g
where m is the mass of the person (70 kg) and g is the acceleration due to gravity (approximately 9.8 m/s²).
Substituting the values into the equations:
N = 70 kg * 9.8 m/s² = 686 N
Fk = 0.05 * 686 N ≈ 34.3 N
The force of static friction (Fs) is the maximum frictional force that can be exerted on an object at rest. It can be calculated as:
Fs = μs * N
where μs is the coefficient of static friction. Given that the coefficient of static friction is 0.35, we can calculate the maximum static friction force as:
Fs = 0.35 * 686 N ≈ 240.1 N
Since the person is already in motion, static friction is not initially exerted. Once the force of kinetic friction decreases the speed of the person to zero, static friction will take over to prevent further motion.
To determine the distance the person will slide before stopping, we can use the work-energy principle. The work done by the force of friction will be equal to the change in kinetic energy of the person.
The work done by friction (W) can be calculated using the equation:
W = F * d
where F is the force of friction (34.3 N) and d is the distance the person slides before stopping.
The change in kinetic energy (ΔKE) can be calculated as the initial kinetic energy (KEi) minus the final kinetic energy (KEf):
ΔKE = KEi - KEf = 0 - 0.5 * m * v^2
where m is the mass of the person (70 kg) and v is the initial velocity of the person (2 m/s).
Since W = ΔKE, we can set up the equation:
34.3 N * d = 0.5 * 70 kg * (2 m/s)^2
Simplifying the equation:
34.3 N * d = 0.5 * 70 kg * 4 m^2/s^2
34.3 N * d = 140 kg * m^2/s^2
Now, solve for d:
d = (140 kg * m^2/s^2) / 34.3 N
d ≈ 4.08 m
Therefore, the person will slide approximately 4.08 meters before coming to a stop on the slippery floor.