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# Physics: A shop sign weighing 245N is supported by a uniform 155N beam

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A shop sign weighing 245N is supported by a uniform 155N beam. Find the tension in the guy wire and the horizontal and vertical forces exerted by the hinge on the beam
708N, 580N, -6N

The tires of a car make 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h. THE tires have a diameter of .90m a) What was the angular acceleration of each tire? b) if the car continues to decelerate at this rate, how much more time is required for it to stop

A figure skater can increase her spin rotation rate from an initial rate of 1.0 rev every 2.0s to a final rate of 3.0rev/s. If her initial moment of inertia was 4.6Kgm's^2 what is her final moment of inertia? How does she accomplish this change?

Two astronauts, one mass 60 and the other 80kg are initially at rest and then they push each other apart. How far apart are they when the lighter astronaut has moved 12 m in outer space?

A bullet is fired vertically into a 1.40kg block of wood at rest directly. above it. IF the bullet has a mass of 29.0g and a speed of 510m/s how high will the block rise after the bulled becomes embedded in it?

145g baseball is dropped from a tree 13,0m above the ground. if it hits the ground with a speed of 8.0m/s what is the average force of resistance on it

A projectile is fired at an angle of 45 degrees from the top of a 165 m cliff with a speed of 175m/s. What will be its speed when it strikes the ground below

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A shop sign weighing 245N is supported by a uniform 155N beam. Find the tension in the guy wire and the horizontal and vertical forces exerted by the hinge on the beam (708N, 580N, -6N)
The forces acting on the beam are shown.
Resolving tension T in the guy wire resolved in horizontal and vertical directions gives horizontal component T cos 35o to the left and Tsin 35o upwards.
Considering equilibrium in horizontal direction we get
------------- (1)
Considering equilibrium in vertical direction we get

Or ------------- (2)
Equating moments (torque) of the forces about hinge point we get

Or
Or T = 406/sin 35o = 708 N
Substituting the value of T in equations (1) and (2) we get

And
The tires of a car make 85 revolutions as the car reduces its speed uniformly from 90km/h to 60km/h. THE tires have a diameter of .90m
a) What was the angular acceleration of each tire?
Like equations of motion for translational motion we can write equations for rotational motion as

And
90 km/h = 90*5/18 = 25 m/s and thus
And 60 km/h = 60*5/18 = 16.67 m/s and thus
Substituting in third equation we get

Gives
b) if the car continues to decelerate at this rate, how much more time is required for it to stop
Using first equation of motion we get

Or t = 23 s

A figure skater can increase her spin rotation rate from an initial rate of 1.0 rev every 2.0s to a final rate of 3.0rev/s. If her initial moment of inertia was 4.6Kgm's^2 what is her final moment of inertia? How does she accomplish this change?

As there is no external torque acting on her (frictionless floor), her angular momentum remains conserved and thus

Gives
This change in moment of inertia is done by bringing her stretched arms and legs closer to her axis of rotation.

Two astronauts, one mass 60 and the other 80kg are initially at rest and then they push each other apart. How far apart are they when the lighter astronaut has moved 12 m in outer space?

If we consider the two as a system than there is no external force acting on the system and thus their center of mass does not changes its position. Hence we can write

Or
Or
Or
Means the other is moving 9 m in opposite direction and thus they are
12+9 = 21 m apart

A bullet is fired vertically into a 1.40kg block of wood at rest directly. above it. IF the bullet has a mass of 29.0g and a speed of 510m/s how high will the block rise after the bulled becomes embedded in it?
As the bullet hits it momentarily, no external force acting on it and hence conserving linear momentum the velocity v of combined mass just after impact is given by
(M +m) v = m v0
Or (1.40 + 0.029) v = 0.029*510
Or v = 10.35 m/s
The height attain to come to rest at highest point is thus given by
V2 = u2 + 2as
Or 0 = (10.35)2 + 2(-9.8)h
Gives h = 5.47 m

145g baseball is dropped from a tree 13,0m above the ground. if it hits the ground with a speed of 8.0m/s what is the average force of resistance on it

The acceleration of the ball is given by (downwards positive)
v2 = u2 + 2 a s
Or 8.02 = 0 + 2*a*13.0
Or a = 2.46 m/s2
The forces are the weight of the ball and resistance force F
Thus writing equation of motion according to second law we get
Mg - F = Ma
Or F = Mg - Ma = 0.145(9.8 - 2.46) = 1.06 N

A projectile is fired at an angle of 45 degrees from the top of a 165 m cliff with a speed of 175m/s. What will be its speed when it strikes the ground below

Resolving its initial velocity of projection
Horizontal speed of projectile which remains constant throughout the motion
Vx = 175 cos 45o = 123.7 m/s
And initial vertical velocity
Vyo = 175 sin 450 = 123.7 m/s
As the final vertical position of the projectile is 165 m downwards (upward positive)
Its speed at the ground is given by
vy2 = vyo2 + 2*(-9.8)*(-165)
Or vy2 = 15302 + 3234 = 18536
Or vy = 136.1 m/s
And hence the final velocity with which it strike ground is given by

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