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Calculate the magnitude of the force required to give a 0.145-kg baseball an acceleration a = 1.00 m/s^2 in the direction of the baseball’s initial velocity when this velocity has a magnitude of (a) 10.0 m/s; (b) 0.900c; (c) 0.990c. (d) Repeat parts (a), (b), and (c) if the force and acceleration are perpendicular to the velocity.

Short Answer

Expert verified

The magnitude of forces when the force and the acceleration are along the same line to the velocity..

a)F=0.145N

b)F=1.75N

c)F=51.7N

d)Where the force and the acceleration are perpendicular to the velocity.

a) F=0.145N

b) F=0.333N

c) F=1.03N

Step by step solution

01

Step 1:Formula of magnitude of the force.

When force and acceleration in same line,

F=γ3ma

When force and acceleration are perpendicular.

F=γma

In both the cases,

γ=11-u2c2

02

Step 2:Calculating the force of magnitude when along the same line.

a)

F=11-1023×10820.145*1=0.145N

b)

F=11-0.900c2c20.145*1=1.75N

c)

F=11-0.990c2c20.145*1=51.7N

03

Calculating the force of magnitude when perpendicular to each other.

d)

a) F=11-1023×10820.145*1=0.145N

b)F=11-0.900c2c20.145*1=0.333N

c)F=11-0.990c2c20.145*1=1.03N

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