Consequences of Special Relativity quiz

Abby is watching Bob. In this situation:

• (C) is (K') and (B) is (K)

• (A) is (K') and (B) is (K)

• (B) is (K') and (A) is (K)

• (C) is (K') and (A) is (K)

Answer explanation

Bob is moving in Abby's reference frame so he gets the '

Assume all velocities are relativistic

Bob is holding a stick, and Abby understands that the stick will undergo LENGTH CONTRACTION in their reference frame.
Abby uses the LENGTH CONTRACTION equation (L = 𝛄^-1 Lo).

For Abby the length of the stick in Bob's reference frame is

• L

• Lo

• x'

• 𝛄

Answer explanation

Lo is always the length of the object in question in the reference frame where it is a rest.

Assume all velocities are relativistic. The first letter after V is the frame it is defined in, and the second is the frame it is with respect to.

Chuck runs by Bob at a speed V_CB. To Figure out Chuck's Speed in Abby's reference frame Abby's uses relat_ivistic velocity addition.
In the velocity addition equation: Ux = (Ux' + v) / (1 + Ux' * v /c²)
V_CB would be

• Ux'

• v

• Ux

• -v

Answer explanation

V_CB is measured with respect to referece frame B.
Since referece frame B is moving with resepct to Abby it must be Ux'. V in this case would be V_BA

Assume all velocities are relativistic. The first letter after V is the frame it is defined in, and the second is the frame it is with respect to.

In Chuck's reference frame, the answer that Abby got for his velocity, Ux' in the last equation, would be (mark all that apply):

• V_CB + V_BA

• V_CB-V_BA

• V_AC

Assume all velocities are relativistic. The first letter after V is the frame it is defined in, and the second is the frame it is with respect to.

Bob looks at their watch and compares it to Chuck's and Abby's.
Bob notices that:

• His watch is going slower that Abby's and Chuck's

• His watch is going Faster that Abby's and Chuck's

• His watch is going Faster that Abby's but Slower than Chuck's

• All watches tick away at the same rate

Answer explanation

Due to TIME DILATION clocks moving with respect to an observer will always appear to tick slower than clocks at rest with respect to the observer.

Assume all velocities are relativistic. The first letter after V is the frame it is defined in, and the second is the frame it is with respect to.

Bob looks at their watch and compares it to Chuck's and Abby's.
However, he also sees that Chuck is moving away from him faster than Abby (aka: |V_BA| < |V_CB|)
Bob notices that:

• Chuck and Abby's watches tick at the same rate

• Chuck's watch ticks faster than Abby's

• Abby's Watch ticks faster than Chuck's

Answer explanation

The degree of TIME DILATION depends on how fast a clock is moving with respec to an observer.

The faster the clock moves through space, the slower it moves through time.

Assume all velocities are relativistic.

Bob looks at their watch and compares it to Chuck's.
He sees they are the same type of watch.

Bob notices that:

• His watch is the exact same shape as Chuck's

• Chuck's watch looks stretched out in the VCB direction compared to his.

• Chuck's watch looks squished out in the VCB direction compared to his.

Answer explanation

From Bob's perspective, since Chuck's watch is moving with respect to him, it is length contracted in the direction of travel.

Assume all velocities are relativistic.

Bob looks at their watch and compares it to Chuck's. He wants to calculate the effect of Time Dilation in this case: T = 𝛄To

From Bob's perspective:

• His watch owns To

• Chuck's watch owns To

• Abby's Watch owns To

Answer explanation

From Bob's perspective, since Chuck's watch is moving with respect to him his watch owns To.

The moving watch (Chuck's) ticks slower and therefore To<T. Since 1≤𝛄, To must be owned by the moving watch (Chuck's)

Assume all velocities are relativistic.

Both Bob and Chuck have a timer set to 10 seconds on their watch.
Bob sees that his watch reads 12 seconds when he observes that Chuck's timer goes off.

For Chuck:

• His watch reads 10 seconds when he observes Bob's timer go off.

• His Watch reads 12 seconds when he observes Bob's timer go off.

• His Watch reads 8 seconds when he observes Bob's timer go off.

Answer explanation

Time Dilation is Symmetric.

Both see time pass slower on each other's
watches so both see the other's timer go off at the same 12 seconds.

Bob looks at their watch and compares it to Chuck's and Abby's.
However, he also sees that. |V_BA| < |V_CB| << c

Bob notices that:

• As far as Bob can tell, Chuck and Abby's watches tick at the same rate

• As far as Bob can tell, Chuck's watch ticks faster than Abby's

• As far as Bob can tell, Abby's Watch ticks faster than Chuck's

Answer explanation

The degree of TIME DILATION depends on how fast a clock is moving with respect to an observer.

At V << C special relativity reduces to classical physics. This is called the EQUIVALENCE PRINCIPAL.